Question 343130
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The *[tex \Large n\text{th}] odd number is *[tex \Large 2n\ -\ 1]


The *[tex \Large m\text{th}] odd number is *[tex \Large 2m\ -\ 1]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (2n\ -\ 1)(2m\ -\ 1)\ =\ 4nm\ -\ 2n\ -\ 2m\ +\ 1]


Each of the first three terms of the expanded polynomial are divisible by 2, but the last term is not, therefore the entire polynomial has a remainder of 1 when divided by 2.  The expression represents an odd number by definition.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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